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Disclaimer: I'm trying to find out more about some symptoms that could be signs of child sexual abuse - or could be naturally occuring. The case that brings the questions up has been reported to all proper authorities (including the police and the states child protective service). I'm not asking what to do in a case of child abuse. I just want more information on the symptoms.

The question is what are the naturally occurring prevalence rates of these symptoms?

The physical symptoms are:

  1. Frequent masturbation (with full erection)
  2. Masturbation to the point of pain
  3. Bloody penis (foreskin prematurely pulled back)
  4. Rectal prolapse

Why I'm asking the question:

All authorities involved (police, child protective services, court appointed child attorney - aka guardian ad litem, and a judge) have determined that the symptoms are not indicative of abuse. This seems crazy to me - but I realize these symptoms (eg. a 4 year old masturbating) may not be as rare as I thought, so I'd like to understand for myself where they're coming from.

Here's what little I've found and estimated:

  1. Frequent masturbation in 4 years old seems to occur less than 5% of male population. See here and here (or full-text). I have no idea how many of that 5% are also related to abuse vs. naturally occurring.
  2. Excessive/Painful masturbation: Less than 1%.
  3. Prematurely forcing back foreskin: no idea.
  4. Rectal prolapse: Not sure at his age, but this is supposedly most common in 0-2 years or 65+. Otherwise it appears to be about 2.5/100,000 based on this study.

Joint probability Experiencing symptoms (1) and (3) at some point would be 5/100 * 2.5/100,000 = 12.5/10,000,000 - it is likely that fewer than 1 in 1 million children would experience both of these symptoms at some point. Factor in the probability of them happening simultaneously and the odds sky rocket from there. Am I missing something here?

I'd particularly like links to reference-able studies if available. I've had trouble finding reliable sources myself, so the above estimates are based off some surveys and online information I could find.

EDIT: I've completely reformatted the question to try and keep discussion on topic.

EDIT 2: Added some sources.

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    Never mind probabilities, you need to contact the police. Your profile suggests you're in the US, so the state the child lives in has an agency that deals with exactly this sort of thing. You need to be talking to them, not strangers on the internet. Please do so because we can't provide answers to questions like this here. – Carey Gregory♦ Jun 16 '18 at 0:32
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    I agree with @CareyGregory. As someone who works with the abused I can categorically say it is definitely a police matter, and as someone who has knowledge of possible abuse, you have a legal duty in the US to report it, otherwise you can be held equally culpable. File a report and let the police investigate it. – Chris Rogers Jun 16 '18 at 7:01
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    I'm voting to close this question as off-topic because this is a question for authorities. We are not the police, and probabilities are irrelevant. Even if we tell you how likely it is, (usually) the police will investigate anyway and discard us claiming anything. Please go with this to the police ASAP. – Narusan Jun 16 '18 at 7:39
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    Yes, everything you've described is very likely indicative of sexual abuse. Have you contacted the state's department of child protective services? You need people involved who don't care who or what the suspected abuser is. – Carey Gregory♦ Jun 16 '18 at 22:31
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    You do exactly what you did. Now you have 3 reopen votes, including mine. – Carey Gregory♦ Jun 19 '18 at 1:05

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